/*!
 * \file CBezierBlending.cpp
 * \brief Subroutines for Bezier blending for FFDs
 * \author F. Palacios, T. Economon, S. Padron
 * \version 7.1.0 "Blackbird"
 *
 * SU2 Project Website: https://su2code.github.io
 *
 * The SU2 Project is maintained by the SU2 Foundation
 * (http://su2foundation.org)
 *
 * Copyright 2012-2020, SU2 Contributors (cf. AUTHORS.md)
 *
 * SU2 is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * SU2 is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with SU2. If not, see <http://www.gnu.org/licenses/>.
 */

#include "../../include/grid_movement/CBezierBlending.hpp"
#include "../../include/option_structure.hpp"


CBezierBlending::CBezierBlending(short val_order, short n_controlpoints){
  SetOrder(val_order, n_controlpoints);
}

CBezierBlending::~CBezierBlending(){}

void CBezierBlending::SetOrder(short val_order, short n_controlpoints){
  Order  = val_order;
  Degree = Order - 1;
  binomial.resize(Order+1, 0.0);
}

su2double CBezierBlending::GetBasis(short val_i, su2double val_t){
  return GetBernstein(Degree, val_i, val_t);
}

su2double CBezierBlending::GetBernstein(short val_n, short val_i, su2double val_t){

  su2double value = 0.0;

  if (val_i > val_n) { value = 0.0; return value; }

  if (val_i == 0) {
    if (val_t == 0) value = 1.0;
    else if (val_t == 1) value = 0.0;
    else value = Binomial(val_n, val_i) * pow(val_t, val_i) * pow(1.0 - val_t, val_n - val_i);
  }
  else if (val_i == val_n) {
    if (val_t == 0) value = 0.0;
    else if (val_t == 1) value = 1.0;
    else value = pow(val_t, val_n);
  }
  else {
    if ((val_t == 0) || (val_t == 1)) value = 0.0;
    value = Binomial(val_n, val_i) * pow(val_t, val_i) * pow(1.0-val_t, val_n - val_i);
  }

  return value;
}

su2double CBezierBlending::GetDerivative(short val_i, su2double val_t, short val_order_der){
  return GetBernsteinDerivative(Degree, val_i, val_t, val_order_der);
}

su2double CBezierBlending::GetBernsteinDerivative(short val_n, short val_i, su2double val_t, short val_order_der){

  su2double value = 0.0;

  /*--- Verify this subroutine, it provides negative val_n,
   which is a wrong value for GetBernstein ---*/

  if (val_order_der == 0) {
    value = GetBernstein(val_n, val_i, val_t); return value;
  }

  if (val_i == 0) {
    value = val_n*(-GetBernsteinDerivative(val_n-1, val_i, val_t, val_order_der-1)); return value;
  }
  else {
    if (val_n == 0) {
      value = val_t; return value;
    }
    else {
      value = val_n*(GetBernsteinDerivative(val_n-1, val_i-1, val_t, val_order_der-1) - GetBernsteinDerivative(val_n-1, val_i, val_t, val_order_der-1));
      return value;
    }
  }

  return value;
}

su2double CBezierBlending::Binomial(unsigned short n, unsigned short m){

  unsigned short i, j;
  su2double result;

  binomial[0] = 1.0;
  for (i = 1; i <= n; ++i) {
    binomial[i] = 1.0;
    for (j = i-1U; j > 0; --j) {
      binomial[j] += binomial[j-1U];
    }
  }

  result = binomial[m];
  if (fabs(result) < EPS*EPS) { result = 0.0; }

  return result;

}
